Effect of different initializations on EKM algorithm

As an integral part of interval type-2 fuzzy logic system (IT2FLS), type reduction (TR) plays a vital role in determining the performance of IT2FLS. Out of many type reduction algorithms, only Karnik-Mendel type TR algorithms capture the essence of interval type-2 fuzzy sets in type reduction. Enhanced Karnik-Mendel (EKM) algorithm is the most commonly used TR algorithm. In this work, we propose three new initializations for EKM algorithm. It is shown they are performing better than EKM and one of the proposed initializations significantly outperforms others. The performance gain can be upto 40% as per comprehensive simulation results demonstrated in this paper. Our findings are justified by computational time savings and iteration requirement for switch point search.

[1]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[2]  Saeid Nahavandi,et al.  Effects of type reduction algorithms on forecasting accuracy of IT2FLS models , 2014, Appl. Soft Comput..

[3]  Jerry M. Mendel,et al.  Enhanced Karnik--Mendel Algorithms , 2009, IEEE Transactions on Fuzzy Systems.

[4]  Robert Ivor John,et al.  The collapsing method of defuzzification for discretised interval type-2 fuzzy sets , 2009, Inf. Sci..

[5]  M. Melgarejo,et al.  A Fast Recursive Method to Compute the Generalized Centroid of an Interval Type-2 Fuzzy Set , 2007, NAFIPS 2007 - 2007 Annual Meeting of the North American Fuzzy Information Processing Society.

[6]  Dongrui Wu,et al.  Computationally Efficient Type-Reduction Strategies for a Type-2 Fuzzy Logic Controller , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[7]  M. Gorzałczany.  Interval-valued fuzzy controller based on verbal model of object , 1988 .

[8]  Jerry M. Mendel,et al.  Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters , 2000, IEEE Trans. Fuzzy Syst..

[9]  Robert Ivor John,et al.  An Investigation into Alternative Methods for the Defuzzification of an Interval Type-2 Fuzzy Set , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[10]  Saeid Nahavandi,et al.  An interval type-2 fuzzy logic system-based method for prediction interval construction , 2014, Appl. Soft Comput..

[11]  Dongrui Wu,et al.  Approaches for Reducing the Computational Cost of Interval Type-2 Fuzzy Logic Systems: Overview and Comparisons , 2013, IEEE Transactions on Fuzzy Systems.

[12]  Robert Ivor John,et al.  A Fast Geometric Method for Defuzzification of Type-2 Fuzzy Sets , 2008, IEEE Transactions on Fuzzy Systems.

[13]  Jerry M. Mendel,et al.  Centroid of a type-2 fuzzy set , 2001, Inf. Sci..

[14]  Oscar Castillo,et al.  A review on interval type-2 fuzzy logic applications in intelligent control , 2014, Inf. Sci..

[15]  Jerry M. Mendel,et al.  Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems , 2002, IEEE Trans. Fuzzy Syst..

[16]  Woei Wan Tan,et al.  Towards an efficient type-reduction method for interval type-2 fuzzy logic systems , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[17]  Jerry M. Mendel,et al.  Type-2 fuzzy sets and systems: an overview , 2007, IEEE Computational Intelligence Magazine.

[18]  Hao Ying,et al.  Derivation and Analysis of the Analytical Structures of the Interval Type-2 Fuzzy-PI and PD Controllers , 2010, IEEE Transactions on Fuzzy Systems.

[19]  Jerry M. Mendel,et al.  Uncertainty, fuzzy logic, and signal processing , 2000, Signal Process..

[20]  Dongrui Wu,et al.  Genetic learning and performance evaluation of interval type-2 fuzzy logic controllers , 2006, Eng. Appl. Artif. Intell..

[21]  Saeid Nahavandi,et al.  Prediction interval construction using interval type-2 Fuzzy Logic systems , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[22]  Jerry M. Mendel,et al.  Designing practical interval type-2 fuzzy logic systems made simple , 2014, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[23]  Yeong-Hwa Chang,et al.  Simplified type-2 fuzzy sliding controller for wing rock system , 2012, Fuzzy Sets Syst..

[24]  Dongrui Wu,et al.  A type-2 fuzzy logic controller for the liquid-level process , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[25]  Patricia Melin,et al.  Particle swarm optimization of interval type-2 fuzzy systems for FPGA applications , 2013, Appl. Soft Comput..

[26]  Robert Ivor John,et al.  The sampling method of defuzzification for type-2 fuzzy sets: Experimental evaluation , 2012, Inf. Sci..

[27]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[28]  Hani Hagras,et al.  A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots , 2004, IEEE Transactions on Fuzzy Systems.

[29]  Jerry M. Mendel,et al.  Stability analysis of type-2 fuzzy systems , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[30]  D. Srinivasan,et al.  Interval Type-2 Fuzzy Logic Systems for Load Forecasting: A Comparative Study , 2012, IEEE Transactions on Power Systems.

[31]  Woei Wan Tan,et al.  A simplified type-2 fuzzy logic controller for real-time control. , 2006, ISA transactions.

[32]  Jerry M. Mendel,et al.  Interval type-2 fuzzy logic systems , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[33]  Dongrui Wu.  An overview of alternative type-reduction approaches for reducing the computational cost of interval type-2 fuzzy logic controllers , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[34]  Yuanli Cai,et al.  Advantages of the Enhanced Opposite Direction Searching Algorithm for Computing the Centroid of An Interval Type‐2 Fuzzy Set , 2012 .

[35]  Dongrui Wu,et al.  On the Fundamental Differences Between Interval Type-2 and Type-1 Fuzzy Logic Controllers , 2012, IEEE Transactions on Fuzzy Systems.